An annulus vortex flowmeter for use in conjunction with a subterranean well. A flowmeter includes a housing, a vortex responsive structure which vibrates in response to vortices produced external to the housing and a sensor which senses vibration of the structure and produces a signal indicative of a flow rate. A method of measuring fluid flow rate between a tubular string and a zone intersected by a wellbore includes utilizing a flowmeter having a vortex shedding device external to a housing for interconnection in the tubular string, the flowmeter including a vortex responsive structure which vibrates in response to vortices produced by the vortex shedding device as the fluid flows through an annulus external to the housing, and a sensor which senses vibration of the structure and produces a signal indicative of the rate of flow of the fluid; and determining the flow rate based on the sensor signal.